CSCI E-63C: Week 2 Problem Set

Haberman Survival Dataset

Note how the summary function computes a 5-number summary. The variable surv (survival) is actually a binary categorical variable (yes/no), encoded as 1/2 (in that order, see the haberman.names file). By default, R assumed that those 1 and 2 values are just some numbers (a quantitative variable), so the summary command computes range (quite useless here) etc. If we re-code the values in that column as “yes”/“no” text strings, this does not help much: now summary does not know what to do with them at all (and just tells us that the column contains 306 of some text string values). And finally, when we explicitly make that column a factor (i.e. declare those text strings to be the levels of a categorical variable), the summary command starts counting the numbers of occurences of different levels.

habDat <- read.table("haberman.data",sep=",")
colnames(habDat) <- c("age","year","nodes","surv")
summary(habDat$surv)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   1.000   1.000   1.265   2.000   2.000

# make sure you understand how we convert a column of 1/2 values into "yes"/"no" here:
# we are indexing into a 2 -element vector `c("yes","know")` with the vector of indices
# which is the column data. We get back the vector of the same length as the *index* (i.e.
# we get back as many values as we asked for!), and in every position where the index was saying
# 1 (or 2), the returned vector will have "yes" (or "no", respectively), because are the values
# at those positions in the vactor we are indexing into:
habDat$surv <- c("yes","no")[habDat$surv]
summary(habDat$surv)

##    Length     Class      Mode 
##       306 character character

habDat$surv <- factor(habDat$surv)
summary(habDat$surv)

##  no yes 
##  81 225

Below we show xy-scatterplots of two variables (patient’s age and node count), with color indicating their survival past 5 years. The first example uses basic plotting capabilities in R (built-inbase graphics package), while the second one shows how the same result can be achieved with ggplot2 package.

Note that in this particular example we additionally choose to stratify the data into two separate scatterplots by the survival categorical variable. The reason is purely aesthetic one: since we do indicate distinct classes of patients with different colors it would be entirely possible (and meaningful) to put all the data into a single scatterplot, same way it was done in class. However, the data at hand do not readily separate into (visually) distinct groups, at least in the projection on the two variables chosen here. Hence, there would be too much overplotting (exacerbated by the fact that node counts and years take on integer values only, so we’d probably need to add some jitter). It would be just more difficult to notice that the subset of data shown on the right (survival=yes) is in fact much more dense near nodes=0. It is certainly OK to choose the type of visualization that provides the most insight into the data at hand!

# idiomatic expression: split the figure area into subplots, 1 row/ 2 columns in this case, 
# additionally change the text pointsize for all future plots; save all the old graphics device settings
oldPar <- par(mfrow=c(1:2),ps=16)

for ( iSurv in sort(unique(habDat$surv)) ) {  # for iSurv in ("no", "yes")
  
    # another trick: function plot() will auto-adjust plot limits to the data being plotted. We
    # want the two plots to have the same limits though. One way of doing it is 
    # as shown below: just use the plot() command on the *whole* dataset, thus
    # letting it set the same limits for every plot automatically, but use plot type "n"
    # which results in all the axis being set up but NO DATA being actually plotted. Then,
    # use the points() command to add to that pre-set plot just the datapoints that we actually want 
    # to show. 
    # ALTERNATIVELY: we could use range(habDat$age) and range(habDat$nodes) to get the full ranges
    # of the respective vatiables, then plot with a single plot() command using xlim= and ylim=
    # optional arguments to set the axis limits explicitly.
    plot(  habDat[,c("age","nodes")], type="n", main=paste("Survival:",iSurv))
  
    # vector of TRUE/FALSE values, indicating whether we want each particular data point in the current plot.
    # Here, we select only the observations with survival status equal to the current value of loop variable iSurv:
    selection <- habDat$surv==iSurv
    
    # Add observations with survival status equal to iSurv to the plot. Set their color and shape
    # according to the survival status of each observation. Here, we are using the fact that
    # 'surv' is a factor, so its distinct levels will be enumerated (i.e. encoded with integers).
    # And we can use an integer to specify the plotting color (and point shape too), this would just 
    # refer to the currently installed default palette. In this particular case *all* the points in 
    # each given plot will have the same color and shape, since the plots themselves are already 
    # stratified by levels of 'surv'. But this trick will work in every situation.
    # Note that, interestingly (and unfortunately) enough, when plot() interprets the col= argument
    # and gets a factor, it will automatically use the factor levels (1, 2, 3, ...), not the actual values
    # ("yes"/"no" - those can't be interpreted as colors of course); but the point shape argument pch=
    # does not do it! This is why we had to explicitly force the argument to pch= into integer (to get the
    # factor level for each observation as a factor), but did not have to bother with the color. Alas.
    # Experimantation and debugging will get you there, eventually...
    points(habDat[selection,c("age","nodes")], col=habDat$surv[selection], pch=as.integer(habDat$surv[selection]))
}

# return graphics device to all previous settings, including
# single plotting area (i.e. we remove the split of the area into subplots, in particular)
par(oldPar)

Same plot, using ggplot2 library. The latter uses a paradigm that’s quite different. It works by building up “layers” that you need to “add”, or “stack” on top of each other (literally, using a ‘+’ operator, to build up the object holding the full description of your graph). We start with the “data” layer by specifying the dataset to work with and setting up so-called “aesthetics” - the mappings from the data columns onto x and y variables in the plot, colors, shapes, etc.

In the example below, the aethetics indicate that for each data point (observation) from the data table habDat, the values in age and node columns should become the x and y coordinates, respectively, of the point in the plot, the value from the surv column should become the color (it’s a factor, so in this case ggplot will assign differnt colors to different layers), and the same surv value should also affect the shape of each plotted point (again, each level of the factor will be automatically assigned a different shape).

But that first line only sets up the mappings and does not plot anything. Next we add the geom_point() layer, and by doing so we explicitly specify that now we want to draw points (a scatterplot) using those mappings.

Then we add a command (facet_wrap) that says we actually want to take the scatterplot we built so far and split it into multiple subplots, each corresponding to a unique value of the variabe surv (note that this should be specified as a “formula”, using ~).

Finally, we add a layer of some plot presentation definitions by specifying a “theme” (try removing the last layer and generating a plot without theme_bw()). The command theme_bw() is a convenience shortcut/wrapper, that modifies many things at once. The underlying low(er)-level command that gives you fine-grained control over all the aspects of the figure presentation (axis label, tick label, and title fonts, sizes, and color, text angles, figure background color, and what not) is theme() - just add it to your ggplot object with any figure presentation modifications you like (see help).

ggplot(habDat,aes(x=age,y=nodes,colour=surv,shape=surv)) + 
  geom_point() + 
  facet_wrap(~surv) + 
  theme_bw()

It seems that higher number of nodes might be associated with lower probability of survival: note that despite the fact that in both survival outcomes, yes and no, we have patients with large node counts and the distributions above node count of ~10 look pretty much the same (and structureless too), the survival=yes outcome clearly has much higer fraction of low node count cases, as expected. One attempt to quantify this relationship might involve testing relationship between indicators of survival and count of nodes exceeding arbitrarily chosen cutoffs (e.g. zero or 75th percentile as shown in the example below).
In the example below we first generate a 2-way matrix that cross-tabulates the respective counts of cases with all combinations of survival yes/no and node count zero/non-zero values. As you can see, when nodes=0 is true, the survival yes/no outcomes are split as 117/19, while for subset of cases where nodes=0 is false (i.e. non-zero node count), the survival yes/no values are split as 108/62, which looks much worse (you can check that this difference in survival probability is indeed statistically significant; which statistical test would you use for that?). The second part of the code performs pretty much the same task, except that we stratify the patients with respect to node counts as being above or below 75% percentile, instead of being zero or non-zero (and in that case we see that the survival for the patienst with node count in top 25% percentile is aproximately 50/50, while for the rest of the patients the 5 year survival is 178 vs 39, which is >80% of cases!):

habDat$nodes0 <- habDat$nodes==0
table(habDat[, c("surv","nodes0")])

##      nodes0
## surv  FALSE TRUE
##   no     62   19
##   yes   108  117

habDat$nodes75 <- habDat$nodes>=quantile(habDat$nodes,probs=0.75)
table(habDat[, c("surv","nodes75")])

##      nodes75
## surv  FALSE TRUE
##   no     39   42
##   yes   178   47

Please feel free to model your solutions after the examples shown above, while exercising necessary judgement as to which attributes are best represented as continuous and which ones should be represented as categorical, etc. The descriptions of homework problems provide some guidance as to what is expected, but we leave some of those choices up to you. Making such calls is an integral part of any data analysis project and we will be working on advancing this skill throughout this course.

Lastly – do ask questions! Our discussion board is the best for that

Wireless Indoor Localization Data Set (30 points)

This dataset presents an example of classification problem (room identity) using continuous predictors derived from the strengths of several WiFi signals on a smartphone. More details about underlying data can be found in corresponding dataset description at UCI ML website. To load data into R please use data file wifi_localization.txt available both at the course website and/or in UCI ML dataset repository.

• Once the dataset in loaded into R, please name the data set attributes (variables) appropriately. You have to do it in your code (i.e. programmatically, do not edit the data file before loading by adding the header line).
• Then, determine the number of variables (explain which ones are predictors and which one is the outcome) and observations in the dataset (R functions such as dim, nrow, ncol could be useful for this)
• Generate summary of the data using summary function in R
  
• Generate pairwise XY-scatterplots of each pair of continuous predictors, while indicating the outcome using color and/or shape of the symbols (you may find it convenient to use pairs plotting function).
• Describe your observations and discuss which of the variables are more likely to be informative with respect to discriminating these rooms, i.e. predicting, from the measured signal strenghts, which room the phone is in. What we mean is: literally just look at the plots, for the lack of better methods that we have not developed just yet, and describe which variables you think will be more useful for letting us know which room the smartphone is in.

The last question is not about building a formal classier model (we will get there in due time), but about looking at the data and trying to understand them and to build some intuition/expectations about them.

• Finally, please comment on whether given the data at hand the problem of identifying the room based on the strength of the WiFi signal appears to be an easy or a hard one to solve. Try guessing, using your best intuition, what could be an error in predicting room identity in this dataset: 50%, 20%, 10%, 5%, 2%, less than that? Later in the course we will work with this dataset again to actually develop such a classifier, and at that point you will get a quantitative answer to this question.

Once again, what we are trying to achieve at this time is just to make you think about the data and to provide a (guesstimate) answer just from visual inspection of the scatterplots. Thus, there is no wrong answer at this point, just try your best, explain your (qualitative) reasoning, and make a note of your answer, so you can go back to it several weeks later.

Please reflect on a potential use of such model (predicting room identity on the basis of WiFi signal strength) and discuss some of the limitations that the predictive performance of such a model may impose on its utility. Suppose that we can never achieve perfect identification (it’s statistics after all), so we will end up with some finite error rate. For instance, if this model was integrated into a “smart home” setup that turns the light on or off depending on which room the smartphone is in, how useful would be such model if its error rate was, say, 1%, 10% or 50%?

Can you think of alternative scenarios where this type of model could be used, which would impose stricter or more lax requirements for its predictive performance? The goal here is to prompt you to consider some “bigger picture” aspects that would impact the utility of any particular model – there is no right or wrong answer to this question too, but please do present some kind of summary of your thoughts on this topic (a couple of sentences would suffice, no need for an assay).

#load and name data
wifiLocData = read.table("wifi_localization.txt", header = F, sep="")
colnames(wifiLocData) = c("signal1", "signal2", "signal3", "signal4", "signal5", "signal6", "signal7", "room")

names = names(wifiLocData)

#number of variables
paste("There are", ncol(wifiLocData), "variables and", nrow(wifiLocData), "observations in the dataset.")

## [1] "There are 8 variables and 2000 observations in the dataset."

paste("Predictor:", names[1:7]) 

## [1] "Predictor: signal1" "Predictor: signal2" "Predictor: signal3"
## [4] "Predictor: signal4" "Predictor: signal5" "Predictor: signal6"
## [7] "Predictor: signal7"

paste("Outcome:", names[8])

## [1] "Outcome: room"

#summary
summary(wifiLocData)

##     signal1          signal2          signal3          signal4      
##  Min.   :-74.00   Min.   :-74.00   Min.   :-73.00   Min.   :-77.00  
##  1st Qu.:-61.00   1st Qu.:-58.00   1st Qu.:-58.00   1st Qu.:-63.00  
##  Median :-55.00   Median :-56.00   Median :-55.00   Median :-56.00  
##  Mean   :-52.33   Mean   :-55.62   Mean   :-54.96   Mean   :-53.57  
##  3rd Qu.:-46.00   3rd Qu.:-53.00   3rd Qu.:-51.00   3rd Qu.:-46.00  
##  Max.   :-10.00   Max.   :-45.00   Max.   :-40.00   Max.   :-11.00  
##     signal5          signal6          signal7            room     
##  Min.   :-89.00   Min.   :-97.00   Min.   :-98.00   Min.   :1.00  
##  1st Qu.:-69.00   1st Qu.:-86.00   1st Qu.:-87.00   1st Qu.:1.75  
##  Median :-64.00   Median :-82.00   Median :-83.00   Median :2.50  
##  Mean   :-62.64   Mean   :-80.98   Mean   :-81.73   Mean   :2.50  
##  3rd Qu.:-56.00   3rd Qu.:-77.00   3rd Qu.:-78.00   3rd Qu.:3.25  
##  Max.   :-36.00   Max.   :-61.00   Max.   :-63.00   Max.   :4.00

#pairwise scatterplots
pairs(wifiLocData, col=wifiLocData$room, main = "Wireless Indoor Location Pairwise Data")

for(x in 1:7) {
  plot(wifiLocData$room, wifiLocData[,x], xlab = "Room", ylab = "Signal Strength", main = paste("Signal", x), col = wifiLocData$room, xaxt="n")
  axis(1, seq(1,4, by = 1))
}

Signal 1 is higher in room 2. Signal 2 is not significantly different across the 4 rooms. Signal 3 is the greatest in room 4. Signal 4 is highest in room 2. Signal 5 is highest in room 4. Signal 6 is highest in room 2, and signal 7 is highest in room 2. From the signals highest in room 2, signals 6 and 7 have their peak signals at approximately -60, whereas signals 1 and 4 peak around -10. This suggests that signals 1 and 4 may be the strongest predictors that the phone is in room 2. Signals 3 and 5 both show their peak signal around -40; however, the difference in signal stregth for signal 5 between room 4 and rooms 1-3 in much larger than in room 3, which suggests that signal 5 may be the best predictor that the phone is in room 4.

for(x in 1:7) {
  boxplot(wifiLocData[,x] ~ wifiLocData$room, col=c("lightblue", "thistle", "lightgreen", "pink"), xlab = "Room", ylab = "Signal Strength", main = paste("Signal", x))
}

Identifying the room based on the WiFi signal may be difficult. There is a lot of overlap in the signal strengths between rooms. Given the generated boxplots, Signal 7, for example, shows higher signal strength in room 2. However, the bottom 50% of data points fall within the range of rooms 1 and 3. The same data point could be in the bottom 50% of room 2, the top 75% of rooms 1 and 3, or the top 50% of room 4. This would cause a significantly high error percentage, except in the case where the data point was in the top 50% of room 2 signal strengths. In another example, signal 1 only has much overlap between the bottom 25% of room 2 and the top 50% of room 3, which should decrease the error rate. If 75% of Signal 1 room 2 data points are significantly higher than the other rooms, the error rate may be closer to 25%.

Predicting room identify based on WiFi signal strength may be useful for home energy efficiency, such as controlling heating and air conditioning, or for controlling air purification devices. When a phone is identified as being in a room, the heating/air conditioning could be boosted and the air purification could be triggered. When the phone is far from the room, the energy resource prioritization could be lowered. This may be useful with higher error rates ~20%, compared to controlling the lights, which would only be useful with much lower error rates, ~5%. This is because misfiring of the heating or air purification would not cause as much disturbance as the lights turning on and off incorrectly. Another difficulty that may arise with using this model to control the home is if there are several people in the home, or if the phone and person are not in the same room, causing confusion.

Amount of Fund Raising Contributions (30 points)

While the previous dataset presented an example of a classification problem (where we want to predict a categorical outcome, i.e. the class, or the group, the observation belongs to), here we consider an example of a regression problem. The data are from a direct mail campign, and we aim at predicting dollar amount of a donors’ (next) contribution (which is a number, quantitative variable), based on their demographics and history of past contributions. This dataset is a cleaned up subset of the one used in a data mining competition back in the late 90s. That particular history and use comes with the requirement of describing data source in rather broad and non-specific terms when it is used for educational/competition purposes, so what little information is given to us, that’s it.

To load data into R please use file fund-raising.csv available at the course website in Canvas. Some details about the data attributes can be found in corresponding file fund-raising-notes.txt also available from our course website in Canvas.

• Load the data into R
• Determine the number of variables (explain which ones are predictors – categorical vs. continuous – and which one is the outcome) and observations in the dataset (R functions such as dim, nrow, ncol could be useful for this)
• Generate summary of the data using summary function in R
• Generate pairwise XY-scatterplots of each pair of quantitative attributes.
• Describe your observations and discuss which attributes might be more useful for predicting the outcome as defined in the fund-raising-notes.txt dataset description.

Try being creative: visualizing and discussing potential associations between each of individual (quantitative/continuous) predictor variables and the continuous outcome is relatively straightforward. But this time around you cannot really use the outcome to stratify the points in the pairwise predictor-predictor scatterplots same way we did it in Problem 1: in the latter we had just four possible values of the (categorical) outcome, but now the outcome (donor contribution) is a (potentially continuous) number. There is a finite number of distinct values in each finite-sized dataset, of course, but how many such distinct values are there? Do the plots make much sense and are they even interpretable if you use all those distinct values of contributed amount, as they are? Is there a way around this?

• For extra 5 points study the potential relationships between quantitative and categorical predictors by generating boxplots – no need to generate full set of boxplots for each quantitative/categorical pair, just a few would do (describe your observations in a couple of sentences though).

#load data
fundData = read.table("fund-raising.csv", header = T, sep = ",")
var = names(fundData)
head(fundData)

##   contrib gapmos promocontr mincontrib ncontrib maxcontrib lastcontr  avecontr
## 1       4     12         10          2       15          7         5  4.066667
## 2       5      3         14          3       21          6         5  4.857143
## 3      13     21          5          5       12         17        10 11.000000
## 4      10      6          8          5       10         12        12  9.400000
## 5      10      7          2         10        3         15        10 11.666667
## 6      20      3         16          5       26         15         7  9.576923
##   mailord mindate maxdate age gender
## 1      10    8801    9404  62      F
## 2       5    9312    9404  66      F
## 3       0    9001    9503  69      F
## 4      10    9209    9509  73      M
## 5       0    9511    9508  58      F
## 6      15    9505    8709  85      M

#variables
paste("There are", ncol(fundData), "variables and", nrow(fundData), "observations in the dataset.")

## [1] "There are 13 variables and 3470 observations in the dataset."

paste("Outcome:", var[1])

## [1] "Outcome: contrib"

paste("Continuous/Quantitative Variables:", var[2], var[3], var[4], var[5], var[6], var[7], var[8], var[9], var[12])

## [1] "Continuous/Quantitative Variables: gapmos promocontr mincontrib ncontrib maxcontrib lastcontr avecontr mailord age"

paste("Categorical/Qualitative Variables:", var[10], var[11], var[13])

## [1] "Categorical/Qualitative Variables: mindate maxdate gender"

#subset of only continuous variable data
contVar = subset(fundData, select = -c(mindate, maxdate, gender))

#summary
summary(fundData)

##     contrib           gapmos         promocontr      mincontrib    
##  Min.   :  1.00   Min.   : 0.000   Min.   : 0.00   Min.   : 0.000  
##  1st Qu.: 10.00   1st Qu.: 4.000   1st Qu.: 3.00   1st Qu.: 3.000  
##  Median : 13.00   Median : 6.000   Median : 6.00   Median : 5.000  
##  Mean   : 15.29   Mean   : 7.819   Mean   : 6.57   Mean   : 5.607  
##  3rd Qu.: 20.00   3rd Qu.:10.000   3rd Qu.: 9.00   3rd Qu.: 5.000  
##  Max.   :200.00   Max.   :77.000   Max.   :29.00   Max.   :80.000  
##     ncontrib       maxcontrib        lastcontr        avecontr      
##  Min.   : 1.00   Min.   :   5.00   Min.   :  0.0   Min.   :  2.261  
##  1st Qu.: 6.00   1st Qu.:  11.00   1st Qu.: 10.0   1st Qu.:  7.100  
##  Median :10.00   Median :  15.00   Median : 14.0   Median :  9.894  
##  Mean   :12.34   Mean   :  18.08   Mean   : 14.8   Mean   : 11.162  
##  3rd Qu.:16.00   3rd Qu.:  20.00   3rd Qu.: 20.0   3rd Qu.: 13.197  
##  Max.   :91.00   Max.   :1000.00   Max.   :250.0   Max.   :103.571  
##     mailord           mindate        maxdate          age       
##  Min.   :  0.000   Min.   :8608   Min.   :8312   Min.   : 4.00  
##  1st Qu.:  0.000   1st Qu.:9007   1st Qu.:9401   1st Qu.:50.00  
##  Median :  1.000   Median :9210   Median :9504   Median :64.00  
##  Mean   :  4.439   Mean   :9208   Mean   :9409   Mean   :62.63  
##  3rd Qu.:  5.000   3rd Qu.:9410   3rd Qu.:9511   3rd Qu.:75.00  
##  Max.   :240.000   Max.   :9702   Max.   :9702   Max.   :98.00  
##     gender         
##  Length:3470       
##  Class :character  
##  Mode  :character  
##                    
##                    
## 

#scatterplots
pairs(contVar)

for(x in 2:9) plot(contVar$contrib, contVar[,x], xlab = "total contribution amount", ylab = names(contVar[x]), main = paste(names(contVar[x]), "vs total contribution"))

#correlation
cor = cor(contVar$contrib, contVar[2:9], method = "pearson"); cor

##         gapmos promocontr mincontrib   ncontrib maxcontrib lastcontr  avecontr
## [1,] 0.1121921 -0.2145865  0.4071754 -0.2116295   0.414476  0.746451 0.6630919
##         mailord
## [1,] 0.01859687

barplot(cor, las = 2, ylab = "Pearson correlation")

Given the scatterplots and correlation of each quantitative variable with the outcome, the most valuable variable for prediction contribution is the dollar amount of the donor’s most recent contribution (lastcontr), which has a positive Pearson correlation of 0.746. The next most highly correlated variable is the average dollar amount of the donor’s contributions (avecontr), followed by mincontrib and maxcontrib, which each showed a moderate Pearson correlation of approximately 0.4. Promotioncal mailing campaign contributions (promocontr) and number of contributions (ncontrib) each showed a smaller negative correlation, as seen by the Pearson correlation of approximately -0.21 and the negative slope of the scatterplots. Mail order responses (mailord) does not show any useful predictive power for contribution.

#quantitative/categorical

for(x in 1:9) boxplot(contVar[,x] ~ fundData$gender, ylab = "gender", xlab = names(contVar[x]), outline = F) #removed outliers to visualize means better

Comparing the categorical variable to quantitative variables shows not much difference between males and females. Females show a slightly lower mean contribution, but a slightly higher maximum maxcontrib than males. Females also show a smaller range for mailord and lastcontr compared to males.

Tibbles (extra 5 points)

Fluency in R (as any other programming language) involves ability to look up, understand, and put to use as necessary new functionality that has not been explored before. One of more recent additions to R are so-called tibbles that can be seen as “modern take on data frames”.

To earn extra points offered by this problem, please look up tibble use and contrast their behavior to that of conventional data frame using one of the datasets you have already created above. To earn all points available your solution must include more than one example of substantive differences (same kind of difference illustrated by two datasets counts as one example).

Please also comment (briefly is fine) on why the use of tibbles may result in more robust code (or not, it’s fine if you happen to find tibbles to be in fact clunkier and not resulting in cleaner code - but you have to argue your point, either way).

library(tibble)
tibble = tibble(fundData)

tibble[1,1]; fundData[1,1]

## # A tibble: 1 × 1
##   contrib
##     <dbl>
## 1       4

## [1] 4

typeof(tibble[1,1]); typeof(fundData[1,1])

## [1] "list"

## [1] "double"

The tibble indexes a single data point and outputs it in a visually appealing format with the variable name included (type = list), whereas the traditional dataframe outputs the value alone (type = double).

tibble$gen; fundData$gen

## Warning: Unknown or uninitialised column: `gen`.

## NULL

##    [1] "F" "F" "F" "M" "F" "M" "M" "M" "M" "M" "F" "F" "M" "M" "F" "M" "M" "M"
##   [19] "F" "M" "F" "F" "M" "M" "M" "F" "F" "M" "F" "M" "M" "M" "F" "M" "F" "M"
##   [37] "F" "M" "F" "F" "F" "M" "F" "M" "F" "M" "F" "F" "M" "M" "F" "F" "F" "M"
##   [55] "F" "F" "M" "F" "M" "U" "M" "M" "M" "M" "M" "F" "F" "M" "F" "F" "M" "F"
##   [73] "M" "M" "F" "M" "M" "M" "M" "M" "U" "F" "F" "F" "M" "M" "M" "M" "M" "M"
##   [91] "F" "M" "M" "M" "F" "M" "F" "F" "F" "F" "F" "M" "M" "F" "M" "U" "F" "F"
##  [109] "F" "M" "M" "M" "F" "F" "F" "M" "F" "F" "F" "M" "F" "M" "M" "F" "F" "M"
##  [127] "F" "F" "F" "M" "M" "F" "M" "M" "F" "M" "M" "M" "M" "M" "F" "M" "U" "F"
##  [145] "M" "F" "F" "M" "F" "F" "M" "F" "F" "M" "M" "M" "F" "M" "F" "M" "M" "F"
##  [163] "F" "F" "M" "M" "F" "M" "M" "F" "F" "M" "M" "U" "M" "M" "M" "F" "F" "M"
##  [181] "M" "F" "F" "M" "M" "M" "F" "F" "M" "M" "F" "F" "M" "M" "F" "M" "F" "F"
##  [199] "M" "M" "F" "F" "F" "F" "M" "M" "M" "F" "F" "F" "F" "F" "F" "F" "F" "M"
##  [217] "F" "F" "F" "F" "M" "M" "M" "F" "F" "M" "F" "M" "M" "F" "M" "F" "F" "U"
##  [235] "F" "F" "M" "M" "M" "F" "F" "F" "M" "F" "F" "M" "M" "F" "F" "F" "M" "M"
##  [253] "F" "F" "M" "M" "M" "F" "F" "F" "M" "M" "M" "F" "F" "F" "M" "M" "F" "F"
##  [271] "M" "F" "M" "F" "M" "F" "M" "F" "F" "M" "F" "F" "F" "F" "F" "U" "F" "M"
##  [289] "M" "F" "F" "M" "M" "F" "M" "F" "M" "F" "M" "F" "F" "M" "M" "F" "M" "U"
##  [307] "M" "F" "M" "M" "F" "M" "M" "F" "F" "M" "M" "F" "U" "M" "M" "M" "M" "M"
##  [325] "F" "F" "M" "U" "M" "M" "M" "F" "M" "U" "F" "M" "F" "M" "M" "M" "M" "U"
##  [343] "F" "M" "M" "M" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "F" "M" "M" "M"
##  [361] "F" "F" "F" "F" "M" "M" "M" "F" "F" "F" "F" "F" "F" "F" "M" "U" "M" "F"
##  [379] "F" "F" "F" "M" "M" "F" "F" "F" "M" "F" "F" "M" "M" "M" "M" "M" "M" "M"
##  [397] "M" "F" "F" "M" "F" "M" "M" "F" "F" "F" "F" "F" "F" "U" "F" "M" "M" "F"
##  [415] "M" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "M" "F" "M" "M" "F" "F" "F"
##  [433] "M" "U" "F" "M" "F" "F" "M" "M" "M" "M" "F" "M" "F" "F" "M" "M" "M" "F"
##  [451] "M" "U" "F" "F" "F" "F" "M" "M" "F" "F" "F" "M" "F" "M" "F" "M" "F" "F"
##  [469] "F" "F" "F" "M" "F" "U" "M" "M" "M" "F" "F" "M" "F" "F" "M" "M" "F" "M"
##  [487] "M" "F" "F" "F" "M" "F" "M" "M" "F" "M" "M" "F" "F" "F" "M" "M" "F" "M"
##  [505] "M" "F" "M" "F" "M" "M" "U" "M" "F" "M" "M" "F" "M" "F" "F" "F" "F" "M"
##  [523] "F" "M" "M" "M" "M" "M" "F" "M" "F" "M" "M" "F" "F" "F" "F" "M" "U" "F"
##  [541] "F" "F" "M" "M" "F" "M" "F" "M" "F" "F" "M" "F" "M" "F" "M" "M" "F" "F"
##  [559] "U" "F" "F" "F" "F" "F" "M" "F" "F" "F" "F" "M" "M" "M" "F" "F" "M" "M"
##  [577] "F" "M" "F" "F" "F" "M" "F" "F" "F" "M" "F" "F" "F" "F" "F" "M" "M" "F"
##  [595] "F" "M" "F" "F" "M" "F" "U" "F" "F" "M" "F" "F" "F" "F" "M" "F" "F" "F"
##  [613] "F" "U" "M" "F" "M" "F" "M" "F" "F" "M" "M" "M" "M" "F" "M" "M" "U" "M"
##  [631] "F" "M" "F" "M" "U" "F" "M" "M" "F" "F" "F" "F" "M" "F" "F" "F" "M" "M"
##  [649] "M" "F" "F" "F" "M" "F" "F" "M" "F" "M" "F" "M" "M" "F" "F" "M" "M" "M"
##  [667] "M" "M" "M" "F" "M" "F" "M" "M" "M" "F" "F" "M" "F" "M" "F" "F" "M" "F"
##  [685] "F" "F" "M" "M" "M" "M" "F" "M" "M" "F" "M" "F" "M" "F" "M" "F" "F" "F"
##  [703] "M" "F" "F" "F" "M" "F" "F" "M" "F" "M" "M" "M" "F" "F" "M" "M" "F" "U"
##  [721] "F" "F" "F" "F" "M" "M" "M" "F" "F" "F" "M" "M" "F" "F" "F" "F" "M" "F"
##  [739] "F" "F" "M" "M" "F" "M" "M" "F" "F" "F" "F" "M" "M" "M" "M" "M" "F" "F"
##  [757] "M" "F" "F" "M" "M" "F" "M" "M" "M" "M" "F" "M" "F" "F" "M" "M" "F" "F"
##  [775] "F" "M" "F" "F" "M" "F" "M" "M" "M" "F" "M" "M" "F" "F" "F" "M" "M" "M"
##  [793] "F" "F" "M" "M" "F" "F" "F" "F" "F" "F" "M" "M" "M" "F" "F" "M" "M" "M"
##  [811] "F" "M" "F" "F" "F" "F" "F" "M" "F" "F" "F" "F" "M" "M" "M" "F" "M" "M"
##  [829] "F" "M" "F" "F" "M" "M" "F" "M" "M" "F" "M" "F" "F" "F" "M" "M" "F" "U"
##  [847] "M" "F" "M" "F" "F" "F" "M" "M" "F" "M" "F" "F" "F" "F" "M" "F" "F" "M"
##  [865] "F" "U" "F" "F" "F" "M" "F" "M" "F" "F" "F" "M" "F" "F" "M" "F" "M" "M"
##  [883] "M" "M" "M" "F" "F" "F" "M" "U" "F" "F" "F" "F" "F" "M" "F" "M" "M" "F"
##  [901] "F" "M" "F" "F" "F" "F" "F" "F" "F" "M" "F" "M" "M" "M" "F" "F" "F" "F"
##  [919] "M" "F" "F" "U" "F" "U" "M" "F" "F" "M" "F" "M" "F" "F" "F" "M" "F" "M"
##  [937] "M" "F" "M" "F" "M" "F" "F" "U" "F" "F" "M" "F" "M" "F" "M" "F" "F" "F"
##  [955] "F" "F" "M" "F" "F" "M" "F" "F" "F" "M" "M" "M" "M" "M" "F" "M" "F" "F"
##  [973] "F" "F" "F" "F" "F" "M" "F" "M" "M" "F" "M" "F" "F" "F" "F" "F" "F" "U"
##  [991] "F" "F" "M" "F" "M" "M" "M" "F" "M" "M" "F" "M" "F" "F" "M" "M" "M" "F"
## [1009] "M" "M" "M" "F" "F" "F" "F" "M" "M" "F" "F" "F" "M" "F" "F" "F" "M" "F"
## [1027] "U" "U" "M" "M" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "M" "M" "M"
## [1045] "F" "F" "M" "F" "F" "M" "M" "F" "F" "M" "F" "M" "F" "M" "M" "M" "M" "F"
## [1063] "M" "F" "F" "M" "F" "F" "M" "F" "F" "M" "M" "M" "M" "M" "M" "M" "M" "M"
## [1081] "F" "F" "F" "F" "M" "F" "F" "M" "F" "F" "M" "M" "M" "F" "F" "F" "M" "M"
## [1099] "F" "M" "M" "U" "M" "F" "F" "F" "F" "M" "F" "M" "F" "M" "M" "M" "M" "F"
## [1117] "F" "F" "M" "F" "F" "F" "M" "F" "F" "F" "M" "F" "F" "M" "F" "F" "F" "M"
## [1135] "F" "F" "F" "M" "M" "F" "M" "M" "F" "M" "M" "M" "M" "F" "F" "F" "U" "F"
## [1153] "F" "M" "F" "F" "U" "M" "M" "M" "M" "M" "F" "F" "F" "F" "F" "M" "F" "M"
## [1171] "M" "M" "F" "F" "F" "F" "F" "M" "F" "M" "U" "F" "M" "F" "M" "M" "M" "M"
## [1189] "F" "F" "F" "F" "F" "M" "F" "F" "F" "F" "U" "F" "F" "U" "F" "M" "F" "F"
## [1207] "F" "M" "M" "F" "M" "F" "F" "F" "M" "M" "M" "M" "M" "F" "M" "F" "F" "F"
## [1225] "F" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "M" "F" "F" "F" "M" "F" "M"
## [1243] "F" "M" "F" "M" "F" "F" "M" "M" "M" "F" "M" "F" "F" "M" "F" "M" "M" "F"
## [1261] "M" "M" "F" "F" "F" "F" "F" "M" "M" "F" "F" "F" "F" "F" "F" "M" "F" "F"
## [1279] "M" "M" "F" "M" "M" "F" "F" "U" "F" "M" "M" "F" "F" "F" "F" "F" "M" "F"
## [1297] "F" "F" "F" "M" "M" "M" "M" "F" "F" "F" "M" "U" "F" "M" "F" "F" "M" "M"
## [1315] "M" "M" "F" "F" "M" "M" "F" "M" "M" "M" "F" "F" "F" "F" "F" "F" "F" "M"
## [1333] "F" "F" "F" "F" "M" "F" "M" "U" "M" "M" "M" "M" "M" "U" "M" "F" "F" "F"
## [1351] "M" "F" "M" "M" "M" "F" "F" "M" "F" "F" "F" "F" "F" "F" "M" "F" "F" "F"
## [1369] "F" "F" "F" "M" "U" "F" "M" "M" "F" "F" "F" "M" "M" "F" "M" "F" "F" "F"
## [1387] "U" "M" "F" "F" "M" "F" "F" "F" "M" "F" "F" "F" "M" "F" "M" "F" "M" "M"
## [1405] "F" "F" "M" "F" "F" "F" "F" "M" "M" "M" "M" "M" "M" "F" "M" "M" "M" "M"
## [1423] "F" "M" "M" "M" "F" "M" "M" "M" "F" "M" "M" "F" "M" "F" "F" "M" "F" "F"
## [1441] "M" "F" "M" "M" "F" "M" "F" "M" "M" "M" "M" "M" "U" "M" "M" "M" "F" "F"
## [1459] "F" "M" "M" "F" "M" "M" "M" "F" "U" "F" "M" "F" "F" "F" "M" "F" "M" "F"
## [1477] "M" "M" "F" "F" "F" "F" "M" "M" "M" "M" "M" "F" "F" "F" "M" "F" "F" "M"
## [1495] "F" "M" "F" "F" "F" "F" "M" "F" "M" "M" "M" "M" "M" "F" "F" "F" "M" "F"
## [1513] "F" "M" "F" "M" "F" "M" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "M" "F"
## [1531] "F" "M" "M" "M" "M" "F" "M" "M" "M" "F" "F" "F" "F" "U" "F" "F" "M" "M"
## [1549] "F" "F" "F" "F" "F" "F" "F" "U" "F" "F" "M" "M" "M" "M" "F" "F" "F" "M"
## [1567] "F" "F" "F" "M" "F" "F" "F" "M" "M" "F" "U" "F" "M" "F" "U" "F" "U" "F"
## [1585] "F" "M" "F" "M" "F" "M" "F" "M" "M" "F" "F" "F" "M" "F" "M" "M" "F" "F"
## [1603] "M" "M" "M" "M" "M" "F" "F" "M" "M" "F" "F" "M" "M" "M" "M" "M" "F" "M"
## [1621] "M" "M" "F" "M" "F" "M" "F" "F" "F" "F" "F" "F" "M" "F" "M" "F" "M" "U"
## [1639] "M" "F" "F" "F" "M" "F" "M" "M" "F" "F" "U" "M" "M" "M" "F" "F" "M" "F"
## [1657] "M" "F" "F" "F" "M" "M" "M" "M" "M" "M" "M" "M" "F" "M" "F" "F" "U" "M"
## [1675] "F" "F" "M" "U" "F" "F" "M" "F" "M" "M" "M" "M" "F" "F" "F" "M" "M" "F"
## [1693] "F" "M" "M" "M" "F" "M" "M" "M" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F"
## [1711] "F" "F" "F" "M" "M" "F" "M" "F" "F" "M" "F" "F" "M" "F" "M" "F" "U" "M"
## [1729] "M" "F" "F" "M" "M" "M" "M" "M" "M" "F" "M" "F" "F" "M" "M" "F" "M" "F"
## [1747] "M" "F" "F" "M" "M" "M" "M" "M" "F" "M" "M" "F" "F" "F" "M" "F" "F" "M"
## [1765] "M" "F" "F" "M" "M" "M" "F" "F" "F" "M" "F" "F" "F" "F" "M" "F" "M" "M"
## [1783] "F" "M" "M" "M" "F" "F" "F" "F" "F" "F" "F" "F" "M" "F" "M" "F" "M" "U"
## [1801] "F" "F" "F" "F" "F" "M" "M" "F" "F" "F" "M" "F" "M" "F" "F" "F" "F" "F"
## [1819] "M" "F" "M" "F" "F" "F" "F" "M" "F" "F" "M" "F" "M" "M" "F" "F" "F" "F"
## [1837] "M" "M" "F" "M" "F" "M" "M" "M" "F" "M" "M" "M" "F" "F" "F" "M" "F" "M"
## [1855] "F" "F" "U" "F" "F" "F" "F" "F" "U" "M" "F" "F" "M" "M" "M" "F" "F" "M"
## [1873] "F" "F" "F" "F" "M" "F" "M" "M" "M" "F" "F" "F" "F" "M" "F" "M" "F" "F"
## [1891] "F" "F" "M" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "M" "F" "M" "F" "M"
## [1909] "F" "F" "F" "F" "F" "F" "F" "M" "F" "M" "M" "F" "M" "F" "F" "F" "M" "M"
## [1927] "F" "M" "F" "M" "F" "M" "F" "M" "M" "F" "F" "M" "M" "F" "M" "F" "F" "M"
## [1945] "M" "M" "F" "M" "M" "M" "F" "M" "F" "U" "F" "F" "F" "F" "F" "M" "F" "F"
## [1963] "F" "F" "M" "M" "F" "F" "F" "F" "U" "F" "F" "M" "F" "M" "M" "M" "M" "M"
## [1981] "M" "F" "F" "F" "F" "F" "F" "F" "M" "M" "M" "F" "F" "F" "F" "M" "F" "M"
## [1999] "F" "M" "M" "M" "F" "F" "F" "M" "F" "M" "U" "M" "F" "M" "M" "U" "M" "F"
## [2017] "M" "F" "F" "M" "F" "F" "F" "M" "F" "M" "M" "F" "F" "F" "F" "F" "M" "F"
## [2035] "M" "M" "F" "F" "F" "M" "F" "U" "M" "F" "M" "F" "M" "F" "M" "F" "M" "M"
## [2053] "F" "F" "F" "F" "U" "F" "M" "F" "F" "F" "F" "F" "M" "M" "F" "F" "F" "F"
## [2071] "F" "M" "M" "M" "M" "F" "M" "M" "F" "F" "F" "M" "F" "F" "M" "M" "F" "M"
## [2089] "M" "M" "M" "F" "F" "M" "F" "F" "M" "F" "F" "F" "M" "M" "M" "M" "F" "F"
## [2107] "M" "F" "M" "M" "F" "M" "M" "F" "M" "F" "F" "F" "M" "F" "F" "M" "F" "M"
## [2125] "M" "M" "M" "F" "F" "F" "U" "F" "M" "M" "M" "F" "F" "M" "M" "F" "F" "F"
## [2143] "F" "F" "F" "F" "F" "F" "M" "M" "M" "M" "F" "M" "F" "F" "M" "F" "F" "M"
## [2161] "F" "F" "U" "M" "F" "F" "F" "F" "F" "F" "M" "F" "M" "F" "M" "F" "F" "M"
## [2179] "M" "M" "F" "M" "M" "F" "F" "M" "F" "F" "F" "F" "F" "U" "M" "F" "M" "F"
## [2197] "F" "M" "F" "M" "M" "F" "F" "F" "F" "F" "M" "F" "F" "F" "F" "F" "F" "M"
## [2215] "F" "F" "F" "U" "M" "F" "M" "M" "M" "F" "M" "M" "M" "F" "M" "M" "U" "F"
## [2233] "U" "F" "M" "M" "F" "F" "F" "F" "F" "F" "F" "F" "F" "M" "M" "F" "F" "F"
## [2251] "U" "M" "F" "F" "M" "F" "F" "M" "M" "F" "M" "M" "F" "F" "M" "M" "F" "F"
## [2269] "M" "F" "F" "F" "F" "F" "M" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F" "F"
## [2287] "F" "M" "M" "M" "F" "M" "F" "F" "M" "M" "F" "F" "M" "F" "M" "F" "M" "M"
## [2305] "F" "F" "F" "F" "F" "M" "F" "M" "M" "M" "F" "F" "M" "F" "F" "M" "M" "F"
## [2323] "M" "F" "M" "F" "U" "M" "F" "M" "F" "M" "F" "F" "M" "F" "M" "U" "F" "F"
## [2341] "M" "F" "M" "F" "F" "F" "F" "M" "F" "F" "U" "F" "F" "M" "M" "F" "M" "F"
## [2359] "U" "F" "F" "M" "F" "F" "F" "F" "F" "F" "M" "U" "M" "F" "F" "M" "M" "M"
## [2377] "F" "F" "M" "F" "M" "F" "F" "M" "M" "F" "F" "M" "F" "M" "F" "F" "U" "M"
## [2395] "M" "M" "M" "F" "F" "F" "F" "F" "M" "M" "F" "F" "F" "M" "M" "F" "M" "U"
## [2413] "M" "F" "F" "F" "F" "F" "F" "M" "M" "F" "F" "F" "F" "F" "F" "F" "F" "F"
## [2431] "M" "F" "F" "F" "M" "M" "F" "F" "F" "M" "F" "F" "M" "M" "F" "M" "F" "U"
## [2449] "F" "M" "F" "F" "M" "U" "M" "F" "F" "F" "F" "M" "F" "M" "M" "F" "M" "F"
## [2467] "F" "M" "M" "F" "F" "F" "F" "M" "M" "F" "F" "U" "F" "F" "M" "F" "M" "M"
## [2485] "M" "F" "F" "F" "M" "F" "F" "F" "F" "F" "F" "F" "F" "F" "M" "F" "M" "F"
## [2503] "F" "F" "M" "M" "M" "M" "F" "F" "M" "F" "M" "U" "M" "F" "F" "M" "M" "F"
## [2521] "M" "M" "M" "F" "F" "M" "F" "F" "M" "F" "M" "M" "U" "F" "M" "F" "M" "M"
## [2539] "F" "U" "U" "F" "M" "M" "M" "F" "M" "F" "F" "F" "F" "F" "M" "U" "F" "M"
## [2557] "F" "M" "M" "M" "F" "F" "F" "F" "M" "F" "F" "M" "F" "F" "M" "M" "F" "M"
## [2575] "F" "F" "F" "M" "M" "F" "F" "M" "F" "M" "M" "F" "F" "F" "M" "M" "M" "M"
## [2593] "M" "F" "M" "F" "F" "F" "F" "F" "U" "F" "M" "U" "M" "M" "M" "M" "M" "M"
## [2611] "F" "F" "M" "M" "M" "F" "F" "F" "M" "M" "F" "F" "M" "F" "F" "F" "U" "M"
## [2629] "F" "M" "F" "M" "F" "F" "M" "M" "F" "M" "M" "M" "F" "M" "M" "M" "F" "F"
## [2647] "F" "F" "F" "M" "F" "M" "F" "F" "F" "M" "F" "M" "M" "F" "U" "M" "M" "M"
## [2665] "F" "F" "F" "F" "F" "F" "F" "M" "F" "M" "F" "M" "F" "U" "F" "M" "F" "M"
## [2683] "M" "F" "M" "F" "M" "M" "M" "M" "M" "F" "F" "M" "M" "F" "F" "M" "M" "M"
## [2701] "M" "F" "M" "F" "F" "F" "F" "M" "M" "F" "F" "F" "F" "M" "M" "M" "M" "M"
## [2719] "F" "M" "M" "F" "M" "M" "M" "F" "M" "M" "F" "M" "M" "U" "M" "F" "M" "F"
## [2737] "U" "M" "M" "M" "F" "F" "F" "M" "F" "F" "M" "F" "M" "M" "M" "F" "M" "F"
## [2755] "F" "M" "F" "F" "F" "F" "F" "M" "F" "F" "F" "F" "M" "M" "F" "M" "F" "F"
## [2773] "F" "F" "F" "F" "M" "F" "F" "F" "M" "M" "M" "F" "M" "F" "M" "F" "M" "F"
## [2791] "M" "F" "F" "M" "M" "M" "F" "F" "F" "M" "F" "F" "F" "F" "M" "M" "U" "M"
## [2809] "M" "M" "M" "F" "M" "F" "F" "M" "M" "F" "F" "F" "M" "F" "M" "F" "F" "M"
## [2827] "F" "M" "F" "F" "F" "U" "F" "F" "F" "M" "F" "F" "U" "M" "M" "M" "M" "F"
## [2845] "F" "M" "M" "M" "F" "M" "M" "M" "M" "F" "F" "U" "F" "M" "F" "M" "M" "M"
## [2863] "M" "M" "F" "F" "M" "M" "F" "F" "F" "M" "M" "F" "M" "F" "F" "M" "U" "M"
## [2881] "M" "F" "F" "F" "F" "M" "M" "M" "F" "F" "M" "M" "M" "M" "F" "F" "F" "F"
## [2899] "F" "M" "M" "M" "M" "F" "M" "F" "M" "M" "F" "M" "M" "F" "F" "F" "M" "F"
## [2917] "F" "F" "M" "F" "F" "F" "M" "F" "F" "M" "M" "U" "F" "F" "M" "F" "F" "M"
## [2935] "M" "M" "M" "M" "M" "M" "F" "F" "M" "M" "F" "F" "F" "M" "M" "M" "M" "F"
## [2953] "F" "F" "M" "F" "F" "M" "F" "M" "M" "F" "F" "F" "F" "F" "F" "M" "M" "M"
## [2971] "M" "F" "F" "M" "F" "F" "F" "F" "M" "M" "M" "F" "F" "M" "M" "F" "M" "F"
## [2989] "M" "F" "U" "F" "M" "F" "M" "F" "F" "F" "F" "F" "U" "M" "M" "M" "F" "F"
## [3007] "F" "M" "F" "M" "F" "M" "M" "F" "F" "F" "F" "M" "F" "U" "M" "M" "M" "M"
## [3025] "M" "F" "F" "F" "M" "M" "F" "M" "U" "F" "M" "F" "F" "M" "F" "M" "F" "F"
## [3043] "F" "M" "F" "F" "M" "F" "F" "U" "F" "F" "M" "M" "F" "M" "F" "U" "M" "F"
## [3061] "F" "F" "M" "F" "F" "F" "F" "M" "F" "F" "M" "F" "M" "M" "M" "F" "M" "M"
## [3079] "M" "F" "M" "M" "F" "F" "F" "M" "F" "F" "F" "F" "M" "F" "F" "M" "F" "F"
## [3097] "F" "F" "M" "M" "F" "M" "M" "F" "F" "F" "U" "F" "F" "M" "U" "F" "F" "F"
## [3115] "F" "F" "M" "M" "M" "F" "M" "F" "M" "F" "F" "F" "F" "F" "F" "F" "F" "M"
## [3133] "F" "F" "F" "F" "M" "U" "M" "F" "F" "U" "F" "M" "F" "F" "F" "F" "F" "M"
## [3151] "F" "M" "F" "M" "F" "M" "F" "M" "F" "F" "M" "F" "M" "M" "M" "F" "F" "F"
## [3169] "F" "F" "F" "M" "M" "M" "M" "M" "M" "F" "M" "F" "F" "F" "F" "M" "F" "F"
## [3187] "M" "F" "F" "F" "F" "M" "F" "F" "M" "M" "M" "M" "U" "F" "M" "M" "F" "M"
## [3205] "F" "F" "M" "M" "M" "M" "M" "F" "M" "F" "F" "F" "M" "M" "M" "F" "M" "M"
## [3223] "F" "M" "F" "M" "M" "F" "M" "U" "F" "M" "U" "M" "M" "F" "F" "M" "M" "M"
## [3241] "M" "M" "F" "F" "M" "F" "M" "F" "F" "U" "F" "F" "F" "U" "F" "M" "M" "M"
## [3259] "F" "F" "M" "F" "M" "M" "M" "M" "M" "F" "F" "F" "F" "M" "F" "F" "F" "F"
## [3277] "F" "F" "F" "M" "M" "M" "F" "F" "F" "U" "M" "F" "M" "F" "M" "F" "F" "F"
## [3295] "F" "M" "M" "M" "F" "F" "M" "M" "M" "M" "F" "M" "M" "U" "F" "M" "M" "F"
## [3313] "F" "F" "M" "F" "F" "F" "F" "F" "U" "F" "M" "F" "F" "M" "M" "M" "F" "F"
## [3331] "M" "F" "F" "F" "F" "F" "F" "F" "M" "F" "F" "M" "F" "M" "M" "F" "M" "M"
## [3349] "M" "F" "F" "F" "M" "F" "M" "F" "F" "M" "M" "F" "F" "M" "M" "M" "F" "F"
## [3367] "M" "F" "F" "F" "F" "M" "M" "U" "F" "M" "F" "F" "F" "M" "M" "F" "U" "F"
## [3385] "F" "M" "F" "M" "F" "F" "F" "M" "F" "M" "M" "F" "F" "F" "F" "F" "F" "M"
## [3403] "M" "F" "M" "F" "F" "M" "M" "M" "F" "F" "F" "M" "F" "F" "M" "M" "F" "M"
## [3421] "F" "F" "F" "M" "M" "U" "M" "M" "F" "F" "M" "F" "M" "U" "F" "F" "M" "F"
## [3439] "F" "M" "F" "F" "M" "F" "F" "M" "M" "M" "F" "F" "M" "M" "F" "M" "F" "F"
## [3457] "M" "M" "M" "F" "F" "M" "M" "M" "M" "F" "F" "F" "F" "F"

With $, the tibble will only do complete matching, but the dataframe will do partial matching. Given $gen, the tibble gives a warning and returns NULL and the dataset gives the gender column

tibble[,1]; fundData[,1]

## # A tibble: 3,470 × 1
##    contrib
##      <dbl>
##  1       4
##  2       5
##  3      13
##  4      10
##  5      10
##  6      20
##  7      16
##  8      10
##  9      26
## 10      10
## # … with 3,460 more rows

##    [1]   4.00   5.00  13.00  10.00  10.00  20.00  16.00  10.00  26.00  10.00
##   [11]   7.00   3.00  10.00  20.00  26.00  10.00  20.00  60.00  15.00  10.00
##   [21]  10.00  23.00  10.00   6.00  10.00  15.00  20.00   3.00  11.00  20.00
##   [31]  10.00  16.87  23.00   4.00   5.00   2.50  50.00  10.70  35.00  20.00
##   [41]  14.00  10.00  21.00  13.00  10.00  10.00  15.00  10.00  10.00   5.00
##   [51]   5.00  15.00   2.00  16.00  12.00   5.00  25.00  10.00  20.00   4.00
##   [61]  50.00  19.00  40.00  12.00  20.00   5.00  14.00  25.00  15.00  10.00
##   [71]   5.00  12.00  13.00  15.00  12.00  38.00  10.00  25.00  10.00  15.00
##   [81]  25.00  10.00  23.00  25.00  20.00   7.00  15.00  10.00  20.00  18.00
##   [91]  17.00   5.00  12.50  11.00  10.00   5.00  50.00  10.00   5.00   7.50
##  [101]  10.00  14.00  20.00   1.00   4.00  10.00   9.00   7.00  36.00  15.00
##  [111]  20.00  25.00  10.00   5.00  20.00  10.00  20.00  10.00  15.00  19.00
##  [121]  10.00  15.00  25.00  10.00   8.00   5.00  15.00  10.00   6.00   5.00
##  [131]  30.00  20.00  15.00  15.00  10.00   5.00  17.00  22.00  25.00  16.00
##  [141]  21.00  10.00   8.00   4.00  10.00  21.00  10.00  16.00   5.00  20.00
##  [151]  10.00  10.00  20.00  20.00  20.00   4.00  24.00   6.00  15.00  12.00
##  [161]  13.00  25.00  15.00  20.00   3.00   5.00   6.00  20.00  13.00   5.00
##  [171]  15.00   5.00  12.00  16.00   5.00  14.00   7.00  15.00   4.00  20.00
##  [181]  10.00   7.00  15.00  10.00  15.00   6.00  25.00   4.00  12.00  10.00
##  [191]  12.00   3.00   6.00  15.00  10.00  12.00  12.00  30.00   5.00  11.00
##  [201]  20.00  23.00   7.00  30.00  15.00  14.00  10.00   8.00   8.00   8.00
##  [211]  10.00  25.00  21.00  19.00   2.00  11.00  17.00  15.00  11.00  23.00
##  [221]  11.00  25.00  41.00  20.00  14.00  22.00  20.00  20.00  15.00  17.00
##  [231]   5.00  20.00  21.00  10.00   5.00  15.00   5.00  50.00  16.00  10.00
##  [241]  26.00   5.00  12.00  10.00  14.00  15.00  10.00  10.00   8.00  10.00
##  [251]  15.00  10.00   7.00  15.00  25.00  10.00  10.00  20.00  13.00  12.00
##  [261]   2.00  12.00  20.00  25.00  17.00  20.00  10.00  11.00  10.00   5.00
##  [271]  15.00  10.00  10.00   2.00   6.00  10.00  15.00  20.00   5.00  10.00
##  [281]  41.00   5.00  35.00  18.00  14.00  25.00  12.00  51.00  15.00  15.00
##  [291]   9.00   5.00  16.00   4.00  20.00  20.00  24.00  10.00   9.00  17.00
##  [301]  14.00  25.00  15.00  15.00  16.00   5.00  15.00   5.00  20.00   7.00
##  [311]  20.00  10.00   5.00   5.00  20.00  10.00  10.00  15.00  25.00   6.00
##  [321]  15.00  25.00  15.00  11.00   5.00   7.00  10.00  10.00  15.00   6.00
##  [331]  15.00  11.00   9.00  20.00  20.00   5.00  10.00  15.00  10.00  20.00
##  [341]  10.00  25.00  20.00  16.00   5.00  20.00  13.00  28.00  20.00  10.00
##  [351]  22.00  30.00  10.00  25.00  20.00  25.00   5.00  36.00  10.00   5.00
##  [361]   3.00   7.00  10.00   4.00  15.00  50.00   6.00  20.00  10.00  10.00
##  [371]  15.00  12.00  10.00  25.00  11.00  20.00  25.00  20.00  12.00  12.00
##  [381]  10.00  23.00  20.00  25.00  25.00  25.00  17.00   5.00  24.00  40.00
##  [391]  12.00  10.00  20.00  20.00  10.00  11.00  15.00  21.00  10.00  10.00
##  [401]  20.00  30.00  40.00  10.00  43.00  20.00   6.00  51.00  15.00  10.00
##  [411]  21.00  20.00  20.00  15.00  10.00  11.00   5.00  22.00  25.00   5.00
##  [421]  25.00   8.00  25.00   5.00  30.00  40.00  21.00  17.00  14.00  25.00
##  [431]   5.00   7.00  12.00   7.00  10.00  25.00  20.00  35.00  20.00  10.00
##  [441]  11.00   4.00  25.00  10.00  10.00   7.00  25.00  10.00  16.00  35.00
##  [451]  26.00  10.00  50.00  12.00  10.00   3.00  10.00  15.00  11.00  10.00
##  [461]   9.00  30.00  21.00  20.00  31.00  25.00  50.00  10.00   9.00  25.00
##  [471]  11.00 100.00  21.00   8.00  25.00  10.00  10.00   4.00   8.00  32.00
##  [481]   5.00  20.00  23.00  30.00   8.00   5.00  25.00  10.00  33.00   4.00
##  [491]  10.00  30.00  20.00  11.00   5.00  50.00  11.00  10.00  20.00  12.00
##  [501]  20.00  20.00  35.00  10.00  10.00   3.00  15.00  20.00  25.00   5.00
##  [511]  10.00  30.00  25.00   4.00  15.00  30.00  15.00  18.00  20.00  18.00
##  [521]  23.00  10.00   1.00  11.00  10.00  15.00  12.00   9.00  13.00   5.00
##  [531]  12.00  50.00  10.00  10.00  19.00  10.00   2.00  16.00  20.00  10.00
##  [541]   4.00   2.00  16.00  30.00 100.00  20.00  25.00  10.00  17.00  10.00
##  [551]  20.00  20.00  40.00  10.00  20.00   9.00  25.00  12.00  20.00  20.00
##  [561]  10.00  14.00  10.00   7.00  20.00  15.00  20.00  10.00   9.00  20.00
##  [571]  10.00  15.00  15.00   7.00   7.00  15.00  25.00  25.00  17.00   5.00
##  [581]  50.00   5.00   5.00  20.00  10.00  13.00  25.00  21.00  10.00  15.00
##  [591]  10.00  10.00  11.00  20.00   5.00  20.00  10.00  15.00  10.00  15.00
##  [601]  18.00  12.00   8.00  10.00  10.00  25.00  25.00  15.00   7.00  17.00
##  [611]  20.00  11.00  11.00   8.00  20.00   7.00   2.00   6.00  35.00  25.00
##  [621]  13.00  10.00  10.00  15.00  15.00  10.00  15.00  20.00  50.00  18.00
##  [631]   5.00  15.00  50.00  10.00  10.00  50.00  10.00  10.00  45.00   5.00
##  [641]  10.00   3.00  10.00   7.00  15.00  10.00  15.00   7.00  15.00  10.00
##  [651]  20.00   3.00  15.00  11.00  20.00  11.00  16.00  10.00  25.00  30.00
##  [661]  11.00  12.00  10.00  20.00  25.00   5.00  25.00   8.00  17.00  10.00
##  [671]  19.00   8.00  21.00  15.00   5.00  20.00   4.00  25.00   7.00   5.00
##  [681]  11.00   5.00   5.00   6.00  10.00  20.00  21.00  15.00  10.00  10.00
##  [691]  15.00  10.00   6.00  20.00  14.00   4.00   7.00  20.00  16.00  20.00
##  [701]  12.00   8.00  10.00   5.00  15.00  10.00   5.00   3.00  20.00  32.00
##  [711]   6.00   9.00  15.00  10.00  15.00   5.00 100.00  47.00   5.00  12.00
##  [721]   3.00  10.00  15.00  20.00  23.00  50.00  15.00   5.00  25.00   5.00
##  [731]  15.00  20.00  30.00  10.00  10.00   5.00  13.00   5.00  25.00  25.00
##  [741]  16.00   5.00  20.00   5.00  15.00  10.00   8.00  11.00  14.00  15.00
##  [751]   5.00  35.00  10.00  10.00  10.00   4.00   5.00  40.00  10.00  20.00
##  [761]   5.00  12.00  12.50  25.00   7.00  17.00  15.00   5.00  50.00  10.00
##  [771]  30.00   4.00  13.00  18.00  21.00   8.00   5.00  10.00  10.00   5.00
##  [781]  15.00  10.00  10.00   5.00  10.00  37.00   5.00  25.00  38.00   9.00
##  [791]  10.00  10.00  50.00  10.00  20.00   7.00   5.00  15.00  11.00  15.00
##  [801]  15.00  25.00  10.00  15.00  20.00  10.00  25.00   5.00  25.00  20.00
##  [811]   8.00  15.00   3.00   9.00  50.00  10.00  20.00   6.00   5.00  10.00
##  [821]  10.00  17.00  11.00  15.00  20.00  15.00   5.00  20.00  20.00  20.00
##  [831]  20.00  15.00  20.00   5.00  15.00  12.50   6.00  15.00  10.00  20.00
##  [841]  33.00  10.00   5.00   8.00  25.00  10.00   5.00   6.00  38.00  15.00
##  [851]  20.00   5.00  10.00  14.00  14.00  30.00   5.00   5.00  10.00  25.00
##  [861]  15.00  20.00  30.00  18.00  10.00  14.00  10.00   5.00  12.00  15.00
##  [871]   7.00  25.00   6.00   3.00  14.00  20.00   5.00  15.00   9.00  10.00
##  [881]  10.00  10.00  20.00  25.00  10.00  10.00  14.00  11.00  25.00  20.00
##  [891]  20.00   5.00  20.00  10.00  10.00  20.00 100.00  20.00   3.00  18.25
##  [901]  15.00  12.00  40.00  14.00  36.00  15.00  10.00  20.00  10.00  16.00
##  [911]   8.00   5.00  20.00  15.00   7.00  16.00  20.00  15.00  21.00  10.00
##  [921]  50.00   3.00   5.00  21.00  25.00  20.00  20.00  20.00  10.00  10.00
##  [931]  15.00  15.00   5.00  10.00   6.00   8.00  15.00  25.00  15.00  12.00
##  [941]  12.00  20.00   8.00  30.00  16.00  20.00  15.00   5.00  10.00  18.00
##  [951]  25.00  25.00   6.00  10.00  10.00  10.00  25.00  10.00  15.00  10.00
##  [961]   3.00  15.00  15.00   5.00  20.00  10.00   6.00  10.00  11.00   4.00
##  [971]   4.00  20.00  10.00   5.00   5.00   9.00  20.00  17.00  20.00  12.00
##  [981]  25.00  10.00  30.00  10.00   5.00  10.00  18.00  15.00  20.00  20.00
##  [991]   5.00  20.00  11.00  20.00  15.00  27.00  17.00   9.00  12.00   5.00
## [1001]  25.00  23.00  10.00  18.00  10.00  10.00  10.00  14.00   3.00  20.00
## [1011]  15.00   5.00  15.00  16.00  20.00  17.00   5.00   5.00  20.00  13.00
## [1021]   1.00   6.00  15.00  13.92  15.00  10.00  15.00   4.00  24.00  20.00
## [1031]  23.00  15.00   3.00  20.00  25.00  15.00   5.00  12.00   5.00  10.00
## [1041]  20.00  25.00  20.00  20.00  15.00  35.00  12.00  10.00  10.00   6.00
## [1051]  10.00   5.00  10.00  40.00  10.00  10.00   7.00  15.00  32.00  17.00
## [1061]  30.00   3.00  25.00   7.00  13.00  37.00  10.00  14.00  43.00  14.00
## [1071]  16.00  12.00  12.00   8.00  15.00   8.00  20.00  10.00  10.00  15.00
## [1081]  31.00  15.00  10.00  15.00  12.00  20.00  17.00  25.00  20.00  15.00
## [1091]   5.00  25.00  20.00   3.00  10.00   5.00  10.00  30.00  22.00  10.00
## [1101]  16.00  20.00  21.00  11.00  20.00  10.00  10.00   2.00  10.00  10.00
## [1111]   5.00  10.00  10.00   4.00  10.00  15.00  10.00  10.00  15.00  10.00
## [1121]   6.00  14.00  15.00   5.00  12.00  15.00   5.00   8.00   7.00  20.00
## [1131]  13.00  14.00  15.00  20.00  15.00   4.00  12.00  12.00  10.00  20.00
## [1141]   4.00  25.00  12.00  36.00  21.00  10.00  10.00 100.00  15.00  15.00
## [1151]  15.00  28.00  20.00  12.00  15.00  50.00  21.00  30.00  21.00   5.00
## [1161]  10.00  15.00  10.00  15.00  25.00  26.00  10.00  25.00   6.00  19.00
## [1171]  30.00  10.00   3.00   6.00  20.00  10.00   5.00   5.00   9.00  30.00
## [1181]  10.00  21.00  15.00  10.00  20.00   5.00  15.00   5.00  10.00  11.00
## [1191]  15.00  15.00  20.00  16.00   6.00  10.00  10.00  10.00  25.00 100.00
## [1201]  10.00  21.00   9.00  10.00  30.00  25.00  11.00  15.00  10.00   7.00
## [1211]  10.00  15.00  30.00   8.00   7.00  35.00  25.00   9.00  25.00  35.00
## [1221]  10.00  10.00  19.00  15.00  15.00  10.00  10.00  15.00   5.00  30.00
## [1231]   6.00   3.00  12.00  25.00  46.00   5.00  10.00  20.00  20.00   5.00
## [1241]   5.00 200.00   5.00   5.00  15.00  15.00  11.00  12.00  10.00  20.00
## [1251]   8.00  10.00  20.00  25.00  16.00   5.00  10.00   5.00  15.00   5.00
## [1261]  14.00  10.00  15.00  20.00  44.00   3.00  10.00  10.00  23.00   8.00
## [1271]  15.00  11.00  13.00   5.00  21.00  25.00  20.00  25.00   4.00   6.00
## [1281]  10.00  15.00   5.00  10.00  25.00  13.00  15.00   8.00  15.00  37.00
## [1291]  25.00  12.00  10.00  11.00  10.00  20.00  18.00  38.00  10.00   6.00
## [1301]   5.00  20.00   4.00  15.00  20.00   8.00  20.00  75.00  20.00  10.00
## [1311]  10.00  14.00   8.00   7.00  20.00  12.00   5.00  20.00  15.00  20.00
## [1321]   8.00  10.00  15.00  10.00   5.00   5.00   5.00   5.00  20.00  20.00
## [1331]  15.00  21.00  11.00  25.00  14.00  10.00  10.00  25.00  20.00  10.00
## [1341]  16.00  35.00   9.00  15.00  15.00  20.00  12.00  25.00  15.00  25.00
## [1351]  15.00  20.00  53.00  16.00  12.50  20.00  25.00  21.00  20.00  25.00
## [1361]  35.00  15.00   9.00  25.00   7.00  10.00  19.00   5.00  10.00  20.00
## [1371]   4.00   4.00   3.00  13.00  15.00  10.00  10.00  14.00  25.00  10.00
## [1381]  36.00  15.00   5.00   5.00   7.00   4.00  22.00  10.00  25.00  12.00
## [1391]  21.00   6.00  15.00   3.00  10.00  15.00  10.00  10.00  15.00  10.00
## [1401]   6.00  12.00  10.00   5.00  11.00  25.00   2.00  15.00  16.00  12.00
## [1411]  35.00   7.00   5.00 100.00  26.00   5.00  15.00  20.00   4.00  20.00
## [1421]  12.00  15.00   4.00  27.00   8.00  20.00  10.00  10.00  15.00  44.00
## [1431]  20.00   4.00  21.00  20.00  15.00   8.00   5.00  15.00  20.00  10.00
## [1441]   7.00   7.00  20.00   5.00  13.00  10.00  16.00  21.00  10.00  47.00
## [1451]   9.00  35.00  15.00  20.00   5.00  10.00  15.00  50.00  14.00   6.00
## [1461]   8.00  15.00   5.00  17.00   5.00  16.00  10.00  21.00   7.00  11.00
## [1471]  21.00  15.00  10.00   8.00  15.00   2.00  12.00  25.00  10.00  27.00
## [1481]  25.00   7.00  20.00   8.00  25.00  14.00   9.00  12.00  22.00  15.00
## [1491]   5.00  15.00  10.00   5.00  32.00  20.00  14.00  20.00  10.00   5.00
## [1501]  16.00  10.00   8.00  20.00   8.00  14.00   7.00  15.00  20.00  10.00
## [1511]  12.00  25.00  12.00  19.00  16.00  15.00  10.00  15.00   3.00  15.00
## [1521]  10.00  10.00  15.00  10.00   5.00   8.00  20.00   5.00  10.00   3.00
## [1531]  10.00  25.00   5.00  20.00   6.00  10.00   5.00   5.00  15.00  12.00
## [1541]  17.00  10.00  10.00  35.00  16.00  20.00  11.00   6.00  20.00  27.00
## [1551]  10.00  25.00  12.00  20.00  25.00  25.00  10.00  24.00   8.00  25.00
## [1561]   5.00  20.00   4.00  15.00  25.00  22.00  25.00  30.00  11.00  35.00
## [1571]   5.00  12.00  15.00  20.00   5.00  17.00   5.00  15.00  20.00  20.00
## [1581]  15.00   5.00   5.00  12.00  25.00  25.00  10.00  10.00  20.00   5.00
## [1591]  25.00  20.00  20.00   5.00  25.00  10.00  15.00  23.00  12.00  20.00
## [1601]   5.00  10.00  18.00  10.00  20.00  20.00  15.00  20.00   8.00   4.00
## [1611]   6.00  10.00  25.00   7.00  19.00  15.00  19.00  15.00  15.00  20.00
## [1621]  15.00   6.00  15.00  10.00  25.00   8.00  10.00   4.00  10.00  12.00
## [1631]  17.00  10.00  15.00   9.00  12.00  10.00   3.00   7.00  25.00   5.00
## [1641]  15.00   7.00   3.00   9.00  15.00  10.00  20.00  21.00  26.00  20.00
## [1651]   7.00  12.00  12.00  10.00   7.00  10.00  21.00  12.50  36.00   5.00
## [1661]  15.00  50.00  10.00   6.00   5.00   5.00  15.00  14.00   5.00   8.00
## [1671]  10.00  10.00  14.00  10.00  10.00  15.00   5.00  20.00  15.00   6.00
## [1681]   5.00   9.00  20.00  20.00  25.00  12.00  15.00  15.00  12.00  25.00
## [1691]   9.00  10.00  10.00  19.00  11.00  40.00  75.00  40.00  14.00   3.00
## [1701]  20.00  25.00  15.00  10.00  25.00  10.00   5.00  15.00  15.00  25.00
## [1711]   6.00   5.00  15.00   5.00   8.00  15.00  10.00  33.00   3.00  11.00
## [1721]  20.00   5.00  13.00  32.00  25.00   5.00  12.00  25.00  14.00   5.00
## [1731]  10.00  26.00  20.00  20.00   5.00  20.00  10.00  10.00  20.00  10.00
## [1741]   4.00  35.00   5.00  10.00  15.00  20.00   8.00  12.00  10.00   6.00
## [1751]  15.00  11.00   3.00  10.00  10.00  15.00   9.00  50.00  46.00   8.00
## [1761]  16.00  10.00  26.00  40.00   6.00  25.00   7.00  10.00  25.00  20.00
## [1771]   7.00  15.00  16.00  12.00  10.00   5.00  16.00  25.00  12.50  28.00
## [1781]  23.00  10.00  20.00  20.00   9.00  19.00  25.00  15.00  50.00  12.00
## [1791]  30.00   5.00   4.00  20.00  21.00  10.00  15.00  14.00   5.00   7.00
## [1801]   6.00  14.00  10.00  11.00  21.00  21.00  10.00  10.00  16.00   5.00
## [1811]  50.00  17.00  50.00  15.00  21.00  10.00  15.00  20.00  10.00  10.00
## [1821]  13.00  25.00  12.00  15.00   5.00  10.00  12.00   7.00  15.00  15.00
## [1831]  10.00  14.00  10.00   8.00  10.00  15.00  20.00  15.00  10.00  14.00
## [1841]   7.00  15.00  21.00  14.00  15.00  10.00  10.00  15.00  11.00  17.00
## [1851]  10.00  20.00   5.00   3.00  25.00  11.00  20.00   3.00  13.00  25.00
## [1861]  10.00  25.00   5.00  15.00  10.00   7.00  25.00  13.00  17.00  10.00
## [1871]  30.00  14.00  20.00  10.00   8.00   6.00  25.00  15.00  15.00  20.00
## [1881]   5.00   5.00  11.00   5.00  10.00   8.00  10.00  15.00  10.00  15.00
## [1891]  26.00  15.00  15.00   9.00  12.00   5.00  17.00  15.00  17.00  25.00
## [1901]   5.00   5.00  30.00  10.00  15.00  25.00  10.00  10.00   6.00  15.00
## [1911]  20.00  25.00  12.00  21.00  50.00  10.00  35.00  20.00  15.00   4.00
## [1921]   5.00  15.00  14.00  15.00  20.00   7.00  10.00   4.00  10.00  15.00
## [1931]  12.00  15.00  15.00  25.00  20.00  10.00   5.00  30.00  35.00  20.00
## [1941]  15.00  11.00  10.00  16.00  20.00  10.00  12.50  35.00  12.00   5.00
## [1951]  10.00  20.00  21.00  29.00  15.00  10.00   5.00  11.00  15.00  11.00
## [1961]  30.00  20.00   7.00  20.00 100.00  35.00  20.00   6.00  25.00  20.00
## [1971]  15.00  10.00  10.00  15.00  13.00   5.00  15.00  12.00  18.00  20.00
## [1981]  15.00  20.00  25.00  10.00  13.00   6.00  17.50   5.00   6.00   5.00
## [1991]  15.00   7.00   3.00  10.00   5.00  26.00  21.00  15.00  13.00   8.00
## [2001]  20.00  17.00  11.00  30.00  10.00  10.00  10.00  13.00  12.00   5.00
## [2011]   5.00   5.00   3.00  15.00  11.00  20.00  10.00   5.00   6.00   9.00
## [2021]  12.00   4.00   5.00  25.00  15.00  20.00  19.00  15.00  10.00   7.00
## [2031]  15.00   9.00   6.00  10.00   9.00   5.00  10.00   5.00   7.00  14.00
## [2041]  21.00  20.00   5.00  15.00  25.00  25.00  15.00   6.00  10.00  50.00
## [2051]   5.00  16.00  10.00  15.00  13.00   8.00  10.00  22.00  10.00  15.00
## [2061]   5.00   7.00   5.00   5.00  20.00   5.00  10.00  10.00  11.00  10.00
## [2071]  10.00  10.00   6.00   7.00  11.00  20.00   7.00  20.00   6.00   9.00
## [2081]  10.00  15.00   5.00  25.00   5.00  25.00   5.00   5.00  10.00  15.00
## [2091]  15.00  20.00  15.00   5.00  20.00  25.00  25.00  22.00  21.00  30.00
## [2101]   6.00  20.00  30.00  20.00  20.00  40.00   5.00  10.00  15.00  10.00
## [2111]  11.00   6.00  10.00  15.00   5.00  10.00  10.00  10.00   5.00   5.00
## [2121]   5.00   9.00  20.00   6.00  40.00  23.00  17.00  12.00  25.00  20.00
## [2131]  14.00  21.00  25.00  25.00  15.00  16.00  20.00  10.00  15.00  10.00
## [2141]  25.00  10.00  20.00  15.00  22.00  21.00  15.00  15.00   5.00  10.00
## [2151]  21.00   5.00  10.00   5.00  15.00  10.00  20.00   9.00   5.00  10.00
## [2161]  10.00  15.00  10.00  20.00   8.00   3.00  20.00  10.00  20.00  20.00
## [2171]  10.00   5.00   9.00  10.00  20.00  25.00  20.00  15.00  50.00  23.00
## [2181]  35.00  13.00   9.00  15.00  13.00  11.00  20.00   7.00  15.00  15.00
## [2191]  10.00  25.00  10.00  11.00  15.00  15.00   8.00  10.00  10.00  15.00
## [2201]  15.00  20.00  15.00  20.00  20.00  14.00  20.00  15.00  20.00  25.00
## [2211]  20.00  10.00  20.00   9.00   5.00   6.00  10.00  10.00  19.00  25.00
## [2221]  25.00  10.00  50.00  28.00  10.00   5.00  20.00   3.00  20.00  10.00
## [2231]  50.00  25.00  12.00  10.00  10.00   9.00  25.00  50.00  25.00  10.00
## [2241]   5.00  15.00   9.00  10.00  25.00  10.00  10.00  10.00  16.00  25.00
## [2251]  20.00  11.00  20.00  15.00  20.00  11.00   5.00  10.00  15.00  15.00
## [2261]   5.00  20.00  20.00  15.00 200.00   5.00  10.00  17.00  12.00  10.00
## [2271]  14.00  10.00  12.00  15.00  26.00  20.00  19.00   5.00  51.00  25.00
## [2281]  25.00  10.00  10.00  20.00  14.00  14.00  30.00  10.00  10.00  20.00
## [2291]  24.00  15.00  30.00  20.00   3.00  20.00  10.00  30.00  10.00   9.00
## [2301]   9.00   7.00  10.00  15.00  16.00  20.00  21.00  10.00  14.00  20.00
## [2311]  20.00  13.00  12.00  10.00  30.00  15.00  11.00  30.00  10.00  17.00
## [2321]   8.00  10.00  25.00   5.00  16.00  25.00  10.00  15.00   5.00   5.00
## [2331]  15.00  10.00   8.00  15.00  10.00  15.00  15.00  19.00  16.00  50.00
## [2341]  12.00   5.00  50.00  11.00  11.00  15.00   8.00  35.00  25.00   3.00
## [2351]  10.00   6.00  15.00  15.00  20.00  10.00  11.00  17.00  10.00   3.00
## [2361]  10.00   6.00  20.00   4.00  25.00  16.00  30.00  10.00  10.00  21.00
## [2371]  10.00  25.00  13.00  20.00   5.00  10.00  10.00   5.00  10.00  27.00
## [2381]  12.00  20.00  11.00   2.00  10.00   5.00   5.00   6.00  10.00  21.00
## [2391]  25.00  27.00  10.00  21.00  25.00  25.00  10.00  30.00   4.00   5.00
## [2401]  10.00  13.00   5.00  15.00  20.00  10.00  12.00  12.00  10.00  10.00
## [2411]   6.00   3.00   5.00  21.00  12.50  15.00   5.00  15.00  20.00  10.00
## [2421]  10.00   4.00  10.00  12.00  10.00   6.00  35.00   8.00  10.00  17.00
## [2431]  21.00  10.00  10.00  10.00  10.00   7.00  20.00  10.00   5.00  14.00
## [2441]  13.00  10.00  25.00  20.00   5.00  10.00  20.00  10.00   5.00  10.00
## [2451]  15.00  12.00  10.00  19.00   7.00   5.00   3.00  20.00  10.00   5.00
## [2461]  21.00   5.00  15.00  30.00  10.00  25.00   3.00  35.00  15.00  20.00
## [2471]  13.00   5.00  25.00  10.00  25.00  15.00  15.00   7.00  25.00  16.00
## [2481]   8.00   5.00   3.00   8.00  15.00   5.00  20.00  10.00  25.00   9.00
## [2491]  20.00  20.00  10.00   8.00  10.00  15.00  10.00  10.00  11.00  10.00
## [2501]  15.00  26.00  20.00  15.00  20.00  10.00  25.00  25.00 100.00   5.00
## [2511]   5.00  23.00  15.00  10.00  75.00  17.00  20.00  45.00  20.00  15.00
## [2521]  11.00  16.00  10.00  25.00  20.00   6.00  11.00  10.00   8.00  10.00
## [2531]  20.00  25.00   2.00  25.00  12.00  15.00  12.00   8.00  22.00   8.00
## [2541]   5.00  20.00  18.00   5.00  25.00   5.00  15.00   3.00   5.00  15.00
## [2551]  25.00  15.00  11.00   5.00  11.00  18.00   5.00  20.00  50.00  18.00
## [2561]  10.00  20.00  15.00  13.00  20.00  15.00  10.00  21.00  10.00  10.00
## [2571]   8.00  26.00   5.00  15.00  12.00  10.00  10.00  10.00  13.00  25.00
## [2581]  10.00  10.00   6.00  15.00  20.00  11.00  20.00  10.00  20.00   5.00
## [2591]  24.00  23.00  12.00  15.00  10.00  19.00  15.00   8.00  10.00  25.00
## [2601] 100.00  10.00   5.00  35.00  17.00  25.00  20.00  20.00  17.00   5.00
## [2611]  20.00  15.00  40.00   3.00  14.00  34.00   7.00  20.00  23.00  16.00
## [2621]  25.00   9.00  20.00  10.00  21.00  20.00  15.00  20.00   7.00  10.00
## [2631]  10.00  20.00  38.00   5.00  11.00  10.00   7.00  20.00  11.00  10.00
## [2641]  30.00  10.00   4.00   5.00  30.00  10.00  10.00   5.00   5.00  23.00
## [2651]  12.00  10.00  10.00  15.00  17.00  15.00  10.00   5.00  15.00   8.00
## [2661]  10.00  10.00  15.00  10.00  30.00  15.00   8.00  10.00  30.00  30.00
## [2671]  10.00  10.00   5.00  30.00  11.00   4.50  15.00  13.00  20.00   5.00
## [2681]   5.00  10.00   3.00   5.00  30.00   8.00  10.00  18.00  20.00  23.00
## [2691]   4.00  10.00  20.00  12.00  10.00  20.00  10.00  20.00  20.00  10.00
## [2701]   5.00  15.00  10.00  17.00  16.00   3.00   5.00  20.00  10.00  25.00
## [2711]  10.00  20.00   5.00  15.00   5.00  30.00  23.00  10.00  25.00  13.00
## [2721]   5.00  15.00  25.00   3.00  11.00  25.00   4.00  17.00  10.00  15.00
## [2731]  12.00  10.00  15.00  21.00   9.00  15.00   4.00  17.00  20.00  25.00
## [2741]   6.00  20.00   5.00  18.00  14.00  21.00  20.00  25.00  15.00  25.00
## [2751]  20.00   2.00  37.00  20.00  15.00  15.00  10.00  12.00   7.00  15.00
## [2761]   5.00  10.00   5.00   5.00   5.00  75.00  10.00   5.00  10.00  25.00
## [2771]   5.00  10.00  15.00  10.00  15.00   6.00  25.00  25.00  21.00   2.00
## [2781]   9.00  10.00  15.00  25.00  10.00  18.00   5.00   5.00  20.00  25.00
## [2791]  25.00   5.00  15.00  12.00   5.00   5.00  20.00  10.00   2.00   5.00
## [2801]  11.00  12.00  47.00   6.00  40.00  15.00  16.00  50.00  12.00  10.00
## [2811]  10.00  20.00  10.00  25.00  15.00   5.00   9.00   5.00  15.00  50.00
## [2821]  30.00  12.00  21.00  14.00  25.00  10.00  17.00  25.00  25.00   5.00
## [2831]  10.00  21.00   7.00  24.00   7.00  10.00   4.00  15.00  20.00  15.00
## [2841]  23.00   8.00  10.00   5.00  14.00  25.00  14.00  25.00  25.00  10.00
## [2851]  14.00  10.00  10.00  19.00  36.00  15.00   9.00  10.00   5.00  42.00
## [2861]  20.00  10.00   5.00   5.00  10.00   5.00  12.00  20.00  10.00  20.00
## [2871]  13.00  10.00  50.00  12.00   6.00   9.00  10.00  24.00  11.00  22.00
## [2881]  20.00   6.00   5.00  12.00  11.00  15.00  14.00  10.00  10.00  10.00
## [2891]  10.00  10.00  20.00   4.00  10.00  15.00  12.00  20.00   5.00  21.00
## [2901]  10.00  20.00  11.00  10.00  15.00   7.00  10.00  10.00   5.00  16.00
## [2911]  12.00  25.00  10.00   6.00  26.00  10.00   5.00   4.00  25.00  23.00
## [2921]  23.00   9.00  12.00  32.00  20.00  14.00  15.00  25.00  15.00  15.00
## [2931]  25.00   6.00  10.00  12.00  10.00  10.00  15.00  10.00   6.00  12.00
## [2941]   4.00   9.00   8.00  10.00  10.00  10.00  13.00  20.00  20.00   5.00
## [2951]  37.00  10.00  20.00   9.00  25.00  20.00  10.00  21.00  18.00  12.00
## [2961]  10.00   5.00  23.00  11.00  30.00  10.00  10.00  10.00  20.00  10.00
## [2971]   5.00  10.00  20.00  11.00   5.00  15.00   4.00  20.00  25.00  15.00
## [2981]  21.00   5.00  17.00   6.00  10.00   5.00  13.00   5.00  25.00  15.00
## [2991]   7.00  12.00  30.00  18.00  20.00  25.00  15.00   5.00  60.00   5.00
## [3001]  15.00  15.00   5.00  25.00  20.00  15.00  12.00  22.00  25.00  50.00
## [3011]  10.00   5.00  11.00   8.00   5.00  16.00  26.00  25.00   6.00   6.00
## [3021]   6.00  20.00  10.00  10.00   6.00  10.00  10.00   8.00  15.00  20.00
## [3031]  10.00   5.00   5.00  15.00  15.00  14.00  20.00  10.00  10.00  10.00
## [3041]  10.00  16.00   8.00  15.00  20.00  14.00  17.00  10.00  10.00  19.00
## [3051]  12.00   3.00  10.00  11.00  15.00  15.00  11.00  20.00 100.00  25.00
## [3061]  25.00  15.00  18.00   7.00  19.00   3.00   8.00  40.00  20.00  10.00
## [3071]  20.00   6.00  16.00  10.00   5.00  22.00  20.00  25.00  30.00   5.00
## [3081]  30.00   4.00  15.00  10.00  20.00  10.00  15.00  10.00  16.00  10.00
## [3091]  15.00   5.00  50.00  20.00   6.00   6.00  24.00   5.00  20.00  25.00
## [3101]  10.00  10.00  10.00  15.00   7.00  15.00  20.00   7.00  10.00  14.00
## [3111]  40.00  15.00  10.00  10.00  15.00  11.00  10.00  20.00   7.00  10.00
## [3121]  40.00   8.00  11.00  20.00  40.00   5.00  10.00   5.00  30.00  10.00
## [3131]  11.00  15.00   7.00   8.00  15.00  22.00  14.00  25.00  11.00  30.00
## [3141]  18.00  25.00   5.00   6.00  10.00  25.00  20.00  10.00  10.00  10.00
## [3151]  15.00   5.00   7.00  14.00  15.00  11.00  25.00  15.00  15.00  15.00
## [3161]  10.00  12.00  12.00  25.00   5.00  25.00  10.00  10.00  10.00 100.00
## [3171]  10.00  12.00  45.00   5.00  25.00   8.00   7.00  15.00  10.00  20.00
## [3181]  20.00   8.00  10.00  10.00  15.00  10.00  17.00   4.00  10.00   4.00
## [3191]   5.00  50.00  25.00  23.00  15.00  15.00  12.00  20.00  16.00   8.00
## [3201]  25.00  17.00  10.00  20.00  20.00   5.00  25.00   4.00  10.00   5.00
## [3211]  12.00  16.00  15.00  10.00  21.00  15.00  18.00   5.00  15.00  20.00
## [3221]  16.00   9.00  16.00  53.00  10.00  15.00   6.00   4.00  10.00  12.00
## [3231]  20.00  20.00  10.00  40.00  15.00   8.00  10.00  32.00  12.00   9.00
## [3241]   5.00  12.00   3.00  12.00  55.00   5.00  17.00  16.00  13.00  20.00
## [3251]   5.00  11.00  30.00  20.00  15.00  10.00  10.00   5.00  26.00   8.00
## [3261]   9.00  11.00  10.00  25.00  14.00  10.00   5.00   8.00  26.00  35.00
## [3271]  15.00  10.00  15.00  15.00   8.00  25.00   6.00  30.00  20.00   7.00
## [3281]  20.00  10.00  27.00  30.00  12.00  17.00  15.00  10.00  15.00   5.00
## [3291]   6.00  17.00   5.00  30.00  23.00  13.00  10.00  16.00   7.00  17.00
## [3301]  15.00   4.00   3.00   5.00  15.00  12.00  50.00  20.00  20.00  10.00
## [3311]  10.00  45.00   6.00 102.00  14.00  10.00  10.00  20.00  15.00   6.00
## [3321]  36.00  10.00  10.00  20.00   5.00  15.00   3.00  10.00  10.00  10.00
## [3331]   3.00  10.00  15.00  14.00   5.00   7.00  25.00   5.00   6.00  13.00
## [3341]  18.00   5.00   5.00 100.00   7.00  15.00  15.00   9.00  26.00  10.00
## [3351]  25.00  15.00  26.00   3.00  18.00   6.00  17.00  15.00   6.00  20.00
## [3361]  20.00  25.00  45.00  15.00  10.00  10.00  31.00  20.00  13.00   7.00
## [3371]  25.00  75.00  10.00  15.00   6.00  10.00  20.00  50.00   7.00   5.00
## [3381]  26.00   5.00   9.00  20.00   3.00  20.00  15.00  13.00   5.00  30.00
## [3391]   5.00  10.00  15.00  20.00  12.00   5.00  10.00   2.00   5.00  10.00
## [3401]  25.00  16.00  20.00  10.00  25.00  15.00  10.00  12.00  22.00   5.00
## [3411]  25.00  16.00  25.00  20.00   9.00  10.00  12.00  19.00  10.00  16.00
## [3421]  75.00  20.00  16.00  20.00  17.00  25.00  10.00  10.00  12.50  12.00
## [3431]  36.00   7.00  25.00  10.00  21.00  25.00  38.00  15.00  26.00  12.00
## [3441]  15.00   5.00  25.00  16.00  15.00  20.00   5.00  30.00   5.00  25.00
## [3451]  25.00  10.00   5.00  25.00  15.00   5.00  40.00  12.00  10.00  50.00
## [3461]  15.00  20.00  15.00   7.00  10.00  20.00  15.00   3.00  10.00  18.00

The tibble prints the first 10 rows, making it easier to work with large datasets, compared to the dataframe which outputs the entire column, which is much busier to look at.